Moscow Mathematical Journal
Volume 14, Issue 3, July–September 2014 pp. 617–637.
On Point-Like Interaction of Three Particles: Two Fermions and Another Particle. II
This work continues our previous article, where the construction of Hamiltonian H for the system of three quantum particles is
considered. Namely the system consists of two fermions with mass 1 and
another particle with mass m>0. In the present paper, like before, we
study the part Tl=1 of auxilliary operator T = ⊕∞l=0 Tl involving the construction of the resolvent for the operator H. In this work together with
the previous one two constants 0<m1<m0<∞ were found such that:
1) for m>m0 the operator Tl=1 is selfadjoint but for m≤m0 it has the
deficiency indexes (1, 1); 2) for m1<m<m0 any selfadjoint extension
of Tl=1 is semibounded from below; 3) for 0<m<m1 any selfadjoint
extension of Tl=1 has the sequence of eigenvalues {λn<0, n>n0} with
the asymptotics λn = λ0 eδn + O(1), n → ∞,
where λ0<0, δ > 0, n0>0 and there is no other spectrum on the
interval λ<λn0.
2010 Mathematics Subject Classification. 81Q10, 47S30.
Authors:
R.A. Minlos (1)
Author institution:(1) Institute for Information Transmission Problems of Russian Academy of Sciences, Bolshoy Karetnyi 19, Moscow, Russia
Summary:
Keywords: Selfadjoint extension, Mellin’s transformation, formula of Sokhotsky, boundedness from below, deficincy index.
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